This problem is listed under several book solution manuals, but they\'re wrong.

Question

This problem is listed under several book solution manuals, but they're wrong. Give algorithm in pseudocode

A contiguous subsequence of a list S is a subsequence made up of consecutive elements of S For instance, if S is 5, 15, -30,10, -5, 40, 10, then 15,-30,10 is a contiguous subsequence but 5,15, 40 is not. Give a linear-time algorithm for the following task Input: A list of numbers, a1, a2,..,an. Output: The contiguous subsequence of maximum sum (a subsequence of length zero has sum zero) For the preceding example, the answer would be 10,-5,40,10, with a sum of 55 (Hint: For eachj e 11, 2,..., n), consider contiguous subsequences ending exactly at position j.)

Explanation / Answer

ANSWER

GIVEN BY

Let S be the uninterrupted basics present in a bordering sub-sequence list S.

Give a linear-time algorithm for dilemma

Input:

amount list, al to a„.

Output:

The contiguous sequence of minimum total; if we like, we can presently return the whole, slightly than the sub-sequence.

Note:

a sub-sequence of span 0 has sum 0.

Sub-problem:

Let F(i) be the total of the highest sum adjoining sub-sequence that ends exactly at a,. (But is perhaps of length 0) We crave maxiF(i).

Recursive Formula:

The sub-sequence crucial F(i) either has

(1)length

(2) contains the unsurpassed sub-sequence finishing at a,.1, succeed by element al. Hence, F(1) = max (0, + F(i - 1)). For stability F(0) = 0.

Algorithm:

F(0) = 0 for i = 1 to n: F(i) = max (0,a; + F (i - 1)) return maxi F(i)

Running Time: 0 (n)

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